Application of DerivativeHard
Question
The function f(x)
is
isOptions
A.increasing on (0, ∞)
B.decreasing on (0, ∞)
C.increasing on (0,π / e) , decreasing on (π / e, ∞)
D.decreasing on (0, π / e) increasing on (π / e, ∞)
Solution
Given, f(x)
f′(x)
.....(i)
when x > 0,π + x > e + x
∴ log(π + x) > log(e + x)
and
On multiplying above equations, we get
......(i)
From Eqs. (i) and (ii),
f′(x) < 0
∴ f(x) is decreasing for x ∈ (0, ∞)
f′(x)
.....(i) when x > 0,π + x > e + x
∴ log(π + x) > log(e + x)
and
On multiplying above equations, we get
......(i) From Eqs. (i) and (ii),
f′(x) < 0
∴ f(x) is decreasing for x ∈ (0, ∞)
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